Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Tailoring MXene Thickness and Functionalization for Enhanced Room‑Temperature Trace NO_(2) Sensing

In this study,precise control over the thickness and termination of Ti3C2TX MXene flakes is achieved to enhance their electrical properties,environmental stability,and gas-sensing performance.Utilizing a hybrid method involving high-pressure processing,stirring,and immiscible solutions,sub-100 nm MXene flake thickness is achieved within the MXene film on the Si-wafer.Functionalization control is achieved by defunctionalizing MXene at 650℃ under vacuum and H2 gas in a CVD furnace,followed by refunctionalization with iodine and bromine vaporization from a bubbler attached to the CVD.Notably,the introduction of iodine,which has a larger atomic size,lower electronegativity,reduce shielding effect,and lower hydrophilicity(contact angle:99°),profoundly affecting MXene.It improves the surface area(36.2 cm^(2) g^(-1)),oxidation stability in aqueous/ambient environments(21 days/80 days),and film conductivity(749 S m^(-1)).Additionally,it significantly enhances the gas-sensing performance,including the sensitivity(0.1119Ωppm^(-1)),response(0.2% and 23%to 50 ppb and 200 ppm NO_(2)),and response/recovery times(90/100 s).The reduced shielding effect of the–I-terminals and the metallic characteristics of MXene enhance the selectivity of I-MXene toward NO2.This approach paves the way for the development of stable and high-performance gas-sensing two-dimensional materials with promising prospects for future studies.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

Equilibria of the Abstract Economy under Almost Lower Semi-continuous Assumption

The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

Assistive Devices and Clothing: Exploring Adaptive Clothing Needs for Women with Lower Limb Prostheses Using the FEA Model

This study aimed to comprehensively investigate the essential considerations in designing adaptive clothing for women with lower limb prostheses in Saudi Arabia. Employing a qualitative methodology, the research entailed semi-structured, in-depth interviews with women utilizing lower limb prostheses and prosthetic specialists. This approach was selected to unearth pivotal design prerequisites and comprehend the specific challenges these women encounter within the realm of clothing. The utilization of selective sampling facilitated the collection of intricate and valuable insights. A Functional, Expressive, and Aesthetic (FEA) User Needs model was utilized to scrutinize participant feedback. Functional requisites encompass ease of dressing and undressing, accessibility to the prosthetic limb, comfort, mobility with the prosthesis, and appropriate fit. Additionally, participants highlighted various expressive needs, including privacy preservation, modesty, camouflaging disability appearances, maintaining alignment with non-disabled women’s fashion, and considerations about the aesthetic aspects of garments.

Repetitive transcranial magnetic stimulation for lower extremity motor function in patients with stroke:a systematic review and network meta-analysis

Transcranial magnetic stimulation,a type of noninvasive brain stimulation,has become an ancillary therapy for motor function rehabilitation.Most previous studies have focused on the effects of repetitive transcranial magnetic stimulation(rTMS)on motor function in stroke patients.There have been relatively few studies on the effects of different modalities of rTMS on lower extremity motor function and corticospinal excitability in patients with stroke.The MEDLINE,Embase,Cochrane Library,ISI Science Citation Index,Physiotherapy Evidence Database,China National Knowledge Infrastructure Library,and ClinicalTrials.gov databases were searched.Parallel or crossover randomized controlled trials that addressed the effectiveness of rTMS in patients with stroke,published from inception to November 28,2019,were included.Standard pairwise meta-analysis was conducted using R version 3.6.1 with the“meta”package.Bayesian network analysis using the Markov chain Monte Carlo algorithm was conducted to investigate the effectiveness of different rTMS protocol interventions.Network meta-analysis results of 18 randomized controlled trials regarding lower extremity motor function recovery revealed that low-frequency rTMS had better efficacy in promoting lower extremity motor function recovery than sham stimulation.Network meta-analysis results of five randomized controlled trials demonstrated that highfrequency rTMS led to higher amplitudes of motor evoked potentials than low-frequency rTMS or sham stimulation.These findings suggest that rTMS can improve motor function in patients with stroke,and that low-frequency rTMS mainly affects motor function,whereas high-frequency rTMS increases the amplitudes of motor evoked potentials.More highquality randomized controlled trials are needed to validate this conclusion.The work was registered in PROSPERO(registration No.CRD42020147055)on April 28,2020.

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

NEW METHODS FOR CHARACTERIZING D-η-PROPERLY PREQUASI-INVEX FUNCTIONS

The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.

Relationship between acute high altitude response, cardiac function injury, and high altitude de-adaptation response after returning to lower altitude

The relationship between acute high altitude response (AHAR), cardiac function injury, and high altitude de-adaptation response (HADAR) was assessed. Cardiac function indicators were assessed for 96 men (18 - 35 years old) deployed into a high altitude (3700 - 4800 m) environment requiring intense physical activity. The subjects were divided into 3 groups based on AHAR at high altitude: severe AHAR (n = 24), mild to moderate AHAR (Group B, n = 47) and non-AHAR (Group C, 25);and based on HADAR: severe HADAR (Group E, n = 19), mild to moderate HADAR (Group F, n = 40) and non-HADAR (Group G, n = 37) after return to lower altitude (1,500 m). Cardiac function indicators were measured after 50 days at high altitude and at 12 h, 15 days, and 30 days after return to lower altitude. Controls were 50 healthy volunteers (Group D, n = 50) at 1500 m. Significant differences were observed in cardiac function indicators among groups A, B, C, and D. AHAR score was positively correlated with HADAR score (r = 0.863, P < 0.001). Significant differ- ences were also observed in cardiac function indicators among groups D, E, F, and G, 12 h and15 days after return to lower altitude. There were no significant differences in cardiac function indicators among the groups, 30 days after return to lower altitude, compared to group D. The results indicated that the severity of HADAR is associated with the severity of AHAR and cardiac injury, and prolonged recovery.

A Survey of Lower Limb Rehabilitation Systems and Algorithms Based on Functional Electrical Stimulation

Functional electrical stimulation is a method of repairing a dysfunctional limb in a stroke patient by using low-intensity electrical stimulation.Currently,it is widely used in smart medical treatment for limb rehabilitation in stroke patients.In this paper,the development of FES systems is sorted out and analyzed in a time order.Then,the progress of functional electrical stimulation in the field of rehabilitation is reviewed in details in two aspects,i.e.,system development and algorithm progress.In the system aspect,the development of the first FES control and stimulation system,the core of the lower limb-based neuroprosthesis system and the system based on brain-computer interface are introduced.The algorithm optimization for control strategy is introduced in the algorithm.Asynchronous stimulation to prolong the function time of the lower limbs and a method to improve the robustness of knee joint modeling using neural networks.Representative applications in each of these aspects have been investigated and analyzed.

LOWER SEMICONTINUITY OF A CLASS OF FUNCTIONALSIN SBV_H

In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.

BSDES IN GAMES,COUPLED WITH THE VALUE FUNCTIONS.ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS

We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.

Treatment of Skeletal CL II Patient with Maximum Lower Incisor Protrusion and Minimum Overjet with Rahhal Functional Appliance

Treatment of skeletal Cl II includes functional orthopedic treatment, head-gears, extraction of the upper premolars and orthognathic surgery. To treat any patient with functional appliances (bite jumping) an adequate overjet is necessary. In this case an 11 years old female patient has skeletal CLII due to mandibular deficiency with ANB angle 8 degrees, overbite: 3 mm, overjet: 1 mm, extremely convex profile and underdeveloped chin due to the hyper muscle contraction of the lower lip to obtain oral seal. To obtain an adequate overjet lower first premolars were extracted and maximum retraction using mini screws (for maximum anchorage) was applied. Afterwards Rahhal functional appliance was used by the patient 16 hours a day for 6 months and 10 hours a day for another 6 months for retention. After that fixed orthodontic treatment was completed. Lateral cephalometrics were taken, traced and analyzed. In the result Skeletal CLI was obtained (ANB 4 degree), straight facial profile, normal over bite overjet and particular chin development were noticed. As a conclusion, in skeletal CLII malocclusions, lower incisor protrusion will cause a contraindication for functional treatment. Extraction of the lower premolars and retraction of the lower incisors followed by functional orthopedic treatment is an efficient method to treat these cases instead of waiting for orthognathic surgery, also reducing the muscle pressure on the chin will change the development characteristics of it.

Remark on Some Classes of P-valent Functions

Recently,Aouf and Darwish [1] proved some estimates in relation to the real part of function D k+p-2 f(z)z p for f(z)∈R(1,k,p,α). In this paper we improve their results and obtain the sharp estimation.

Effects of Water Weight-Loss Walking Training on Lower Limb Motor Function and Gait in Stroke Patients

Background: Water weight-loss walking training is an emerging physical therapy technique, which provides new ideas for improving the motor function of stroke patients and improving the quality of life of patients. However, the rehabilitation effect of water weight-loss training in stroke patients is currently unclear. Objective: To analyze the effect of water weight loss walking training in stroke patients. Methods: A total of 180 stroke patients admitted to our hospital from January 2019 to December 2021 were selected and randomly divided into two groups. The control group received routine walking training, and the research group performed weight loss walking training in water on this basis. The lower limb motor function, muscle tone grade, daily living ability, gait and balance ability were compared between the two groups before and after treatment. Results: Compared with the control group, the FMA-LE score (Fugl-Meyer motor assessment of Lower Extremity), MBI score (Modified Barthel Index) and BBS score (berg balance scale) of the study group were higher after treatment, and the muscle tone was lower (P Conclusion: Water weight loss walking training can enhance patients’ muscle tension, correct patients’ abnormal gait, improve patients’ balance and walking ability, and contribute to patients’ motor function recovery and self-care ability improvement.

Associated Hermite Polynomials Related to Parabolic Cylinder Functions

In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. The group-theoretical background with the 3-parameter group of motions M(2) in the plane for Bessel functions and of the Heisenberg-Weyl group W(2) for Parabolic Cylinder functions is discussed and compared with formulae, in particular, for the lowering and raising operators and the eigenvalue equations. Recurrence relations for the Associated Hermite polynomials and for their derivative and the differential equation for them are derived in detail. Explicit expressions for the Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given and by means of them the Parabolic Cylinder functions are represented by two such basic functions.

Multistatic radar analysis based on ambiguity function and Cramér-Rao lower bounds

The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.

Crustal structure along the Zhenkang-Luxi deep seismic sounding profile in Yunnan derived from receiver functions

The crustal thicknesses and the Poisson’s ratios under the seismic stations can be calculated by receiver function method with H-κ stacking effectively. But the stacking results are affected to some extent by the average crustal P-wave velocity. To eliminate this effect and get more accurate crustal structure along the Zhenkang-Luxi deep seismic sounding profile which lies in Yunnan Province, we calculate the receiver functions from the teleseismic events recorded by 11 temporary stations as well as 5 permanent ones along the profile and carry out the stacking with Vp obtained from the profile in this study. Our study shows that the crustal thicknesses along the Zhenkang-Luxi profile range from 34.8 km to 41.8 km with an average of 39 km. The crust is thicker in the middle part of the profile and thinner in both sides in general. Dramatic changes of crustal thickness about 3 km are detected across both the Lancangjiang fault and the Xiaojiang fault, which implies that these faults cut through the Moho. The lowest Poisson’s ratio under the stations is 0.22 and the highest is 0.27 with the mean of 0.25, which is lower than the global average value 0.27 in the continental crust. It suggests that most of the crust along the profile lacks mafic component, but contains more felsic substance. The low Poisson’s ratio also indicates that there is no satisfying condition for partial melting. We deduce that the material flow in the middle-lower crust in the southeastern margin of the Tibetan plateau may occur only in the north region of 24°N.

Effect of Motor Relearning Combined with t DCS on Motor Function of Lower Extremities and Gait in Patients with Cerebral Infarction and 3D Gait Analysis

[Objectives]To observe the effect of motor relearning combined with transcranial direct current stimulation on the motor function of lower extremities in patients with cerebral infarction,and to observe its effect on gait by 3D gait analysis.[Methods]60 patients with cerebral infarction who met the inclusion criteria were randomly divided into 3 groups according to the order of treatment(n=20).Group A received motor relearning treatment,group B received transcranial direct current stimulation treatment,group C received motor relearning combined with transcranial direct current stimulation,and the curative effect was observed after 5 courses of treatment.[Results]Before treatment,FMA,MBI,spatio-temporal parameters for 3D gait analysis(gait frequency,gait cycle,stride length,gait speed,stride length deviation,double support)and lower limb joint motion parameters(affected side stride length,maximum hip flexion,maximum hip extension,maximum knee flexion,maximum knee extension,stance phase,swing phase)were compared among the three groups.After treatment,the FMA and MBI of the three groups increased,and the spatio-temporal parameters for 3D gait analysis(gait frequency,gait cycle,gait speed,double support)and the lower limb joint motion parameters(affected side stride length,maximum hip flexion,maximum hip extension,maximum knee flexion,swing phase)were all improved,while the spatio-temporal parameters(stride length and stride length deviation)and the lower limb joint motion parameters(maximum knee extension and stance phase)decreased.Compared with those before treatment,there were significant differences among the three groups(P<0.05).Through the comparison between groups,it was found that the FMA,MBI,spatio-temporal parameters for 3D gait analysis(gait frequency,gait cycle,gait speed,double support)and lower limb joint motion parameters(affected side stride length,maximum hip flexion,maximum hip extension,maximum knee flexion,swing phase)in group C were significantly higher than those in group A and B,while the spatio-temporal parameters(stride length and stride length deviation)and lower limb joint motion parameters(maximum knee extension and stance phase)in group C were significantly lower than those in group A and group B,and the difference was statistically significant(P<0.05).[Conclusions]Motor relearning combined with transcranial direct current stimulation could increase MBI and FMA,improve gait spatio-temporal parameters and lower limb joint motion parameters,and correct abnormal gait in patients with cerebral infarction.